Quantum bounds on heat transport through nanojunctions

TL;DR

This paper establishes rigorous quantum mechanical bounds for heat transport through nanojunctions, highlighting differences from the quantum of thermal conductance and applicable at high temperatures even with strong interactions.

Contribution

It introduces new quantum bounds on heat current in nanojunctions that are valid at high temperatures and strong interactions, complementing existing low-temperature bounds.

Findings

Bounds are saturated at high temperatures in the quantum regime.

Comparison with numerical models confirms the bounds' validity.

Bounds differ from the quantum of thermal conductance in strongly interacting systems.

Abstract

We derive rigorous quantum mechanical bounds for the heat current through a nanojunction connecting two thermal baths at different temperatures. Based on exact sum rules, these bounds compliment the well-known quantum of thermal conductance $\kappa_Q \equiv \pi k^2_B T/6\hbar$, which provides a bound for low-temperature heat transport in all systems, but is saturated only for noninteracting transport. In contrast, our bounds are saturated at high temperatures---but still in the quantum regime---, even when interactions are very strong. We evaluate these bounds for harmonic and strongly anharmonic junction models and compare with numerical approaches.